Events

Tommaso Pacini, University of Torino

Anisotropic calibrations, adiabatic limits, and mirror symmetry

Calibrations, adiabatic limits and Fueter maps play an important role in the theory of man ifolds with special holonomy and in the corresponding gauge theory. The goal of this seminar is to show how they can be fitted into a very general framework, defined via distributions and the concept of “anisotropic calibrations”. This framework (i) applies in a uniform way across special holonomy, (ii) provides an identification between certain Fueter maps and calibrated submanifolds, (iii) introduces new degrees of freedom which may be useful towards genericity arguments, (iv) provides techniques for both explicit and abstract existence results for Fueter maps. This is joint work with Kotaro Kawai (BIMSA, China). The seminar will be largely non-technical. Details can be found in the arXiv paper with the same title.

MC 5403

Moritz Weber, Saarland University

Quantum Mathematics, quantum symmetries and quantum information

Since the early days of the foundation of quantum mechanics, 100 years ago, it was clear that a new kind of mathematics was needed in order to capture the new physics. At that time, John von Neumann formulated his principles of quantum mechanics and one of the main features was noncommutativity - the fact, that two observables A and B need not to commute. This was the starting point of a systematic study of noncommuting operators which quickly emancipated from "just a physics tool" to an own branch in mathematics as such. More and more often, it is called quantum mathematics nowadays and it comprises C*-algebras (aka quantum
topology), von Neumann algebras (aka quantum measure theory), Connes’s noncommutative geometry (aka quantum differential geometry), quantum groups and many more. I will give a brief survey on quantum mathematics, and I will then focus on an introduction to quantum symmetries and their link to quantum information theory.

MC 5501